Given the expression:
[tex]7y+56[/tex]notice that both coefficients are divisible by 7, then, we can factor the expression like this:
[tex]7y+56=7(y+8)[/tex]Can you help me with number 13? Thank you I am having trouble with it.
In triangle ABC, a is the length of the side opposite to angle A (side BC), b is the length of the side opposite to angle B (side AC), and c is the length of the side opposite to angle C (side AB)
We can use the cosine rule to find the length of each side
[tex]\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ c=\sqrt[]{a^2+b^2-2ab\cos C} \end{gathered}[/tex]From the given figure we can see triangle ABC, where We will use the cosine rule to find c
[tex]c=\sqrt[]{a^2+b^2-2ab\cos 90^{\circ}}[/tex]Since cos(90) = 0, then
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2-2ab(0)} \\ c=\sqrt[]{a^2+b^2-0} \\ c=\sqrt[]{a^2+b^2} \end{gathered}[/tex]The expression equivalent to c is
[tex]\sqrt[]{a^2+b^2}[/tex]verbal expression 19a-3b=16c
We are given the expression 19a-3b=16c and told to write a verbal expression. This verbal expression should describe what is happening in the mathematical expression. Since we are multiplying 19 and a, we can describe this part by "19 times a". Then we are subtracting 3b, so we can say "19 times a minus 3 times b". Finally, we should describe that this expression is equal to 16 multiplied by c. This is achieved with the expression
"19 times a minus 3 times b equals 16 times c"
a radio disc jockey has 8 songs. on the upcoming playlist:2 rock songs3 reggae songs3 country songsthe disc jockey Randomly choose the 1st song to play, then Randomly choose the 2nd song from the remaining ones. what is the Probability that the 1st song is a Rock song? the 2nd song is a Country song?* write as fraction
Probabilities
We have the following elements to choose from:
Rock songs (R) = 2
Reggaes songs (G) = 3
Country songs (C) = 3
It's required to find two probabilities:
a) The first is a rock song
As stated above, there are R = 2 rocks songs and there are 8 songs in total, thus the probability of randomly picking a rock song is:
[tex]\begin{gathered} p(R)=\frac{2}{8} \\ \text{Simplify:} \\ p(R)=\frac{1}{4} \end{gathered}[/tex]b) The second song is a country song.
This is quite more complex to calculate. Let's assume the first song was not a Country song (NC). This has a probability of:
[tex]P(NC)=\frac{5}{8}[/tex]Since there are 5 non-country songs out of 8. For the second pick, we have all of the country songs unplayed out of 7, thus the probability of selecting it is:
[tex]P(C)=\frac{3}{7}[/tex]The probability of this 'brank' of events is:
[tex]P(NC,C)=\frac{5}{8}\cdot\frac{3}{7}=\frac{15}{56}[/tex]Now assume the first song was actually a country song. It has a probability of:
[tex]P(C)=\frac{3}{8}[/tex]For the second pick, we now have only 2 country songs out of 7, so the probability of selecting another country song is:
[tex]P(C)=\frac{2}{7}[/tex]The probability of this 'branch' of events is:
[tex]\begin{gathered} P(C,C)=\frac{3}{8}\cdot\frac{2}{7}=\frac{6}{56} \\ Simplify\colon \\ P(C,C)=\frac{3}{28} \end{gathered}[/tex]The total probability of selecting a country song as the second song is:
[tex]\begin{gathered} P(B)=\frac{15}{56}+\frac{3}{28} \\ P(B)=\frac{15}{56}+\frac{6}{56} \\ P(B)=\frac{21}{56} \\ P(B)=\frac{3}{8} \end{gathered}[/tex]solve for x: In(x+2)= -5
The given equation is:
ln (x + 2) = -5
Take the exponent of both sides
[tex]e^{\ln (x+2)\text{ }}=e^{-5}[/tex]The exponential cancels the ln on the Left Hand Side:
[tex]\text{x + 2 = e}^{-5}[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} \text{x + 2 - 2 = e}^{-5}-2 \\ x=e^{-5}-2 \end{gathered}[/tex]2. If sin B = 3/8, what is tan B?
SInce,
[tex]\begin{gathered} \sin B=\frac{opposite}{hypotenuse} \\ \text{opposite}=3 \\ \text{hypotenuse}=8 \end{gathered}[/tex]Therefore using Pythagoras theorem, we have,
[tex]x=\sqrt[]{8^2-3^2}=\sqrt[]{64-9}=\sqrt[]{55}[/tex]Therefore, tan B can be calculated as,
[tex]\tan \text{ B=}\frac{opposie}{adjacent}=\frac{3}{\sqrt[]{55}}[/tex]Please help me on this :)
The most appropriate choice for Arithmetic series will be given by -
Sum from first [tex]m^{th}[/tex] term to the [tex]n^{th}[/tex] term = [tex]\frac{1}{2}[a_1(n - m)+na_n-ma_m][/tex]
What is arithmetic series?
Arithmetic series is a series where the consecutive terms of the series maintains a constant difference known as the common difference of the series.
If a be the first term of the series and d be the common difference of the series, then [tex]n^{th}[/tex] term of the series [tex]a_n[/tex] is given by
[tex]a_n = a+(n-1)d[/tex]
Here,
The sum of the first n terms of the arithmetic progression =
[tex]\frac{n}{2}(a_1 + a_n)[/tex]
The sum of the first m terms of the arithmetic progression =
[tex]\frac{m}{2}(a_1 + a_m)[/tex]
Sum from first [tex]m^{th}[/tex] term to the [tex]n^{th}[/tex] term = [tex]\frac{n}{2}(a_1 + a_n)[/tex] - [tex]\frac{m}{2}(a_1 + a_m)[/tex]
= [tex]\frac{1}{2}(na_1 + na_n-ma_1-ma_m)[/tex]
= [tex]\frac{1}{2}[a_1(n - m)+na_n-ma_m][/tex]
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this question is just 4 people to get their status up. <333
Answer:
ok
Step-by-step explanation:
ok.............................
1 month bet Rented 3 movies and 2 videos games for a total of $21 the next month she rented 8 movies and four game for a total of $49 find the rental cost for each movie and each video game
Let "m" represent the cost of one movie rent and "v" represent the cost of one videogame rent.
One month she rented 3 movies and 2 videogames for a total of $21, you can express the total cost for this month as:
[tex]3m+2v=21[/tex]Another month she rented 8 movies and 4 video games for a total of $49, you can express the rental costs for this month as follows:
[tex]8m+4v=49[/tex]These expressions form an equation system. To solve it, the first step is to write one of the equations in terms of one of the variables, for example, write the first equation for "v"
[tex]\begin{gathered} 3m+2v=21 \\ 3m-3m+2v=21-3m \\ 2v=21-3m \\ \frac{2v}{2}=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}m \end{gathered}[/tex]Next, replace the expression obtained for "v" into the second equation and solve for "m"
[tex]\begin{gathered} 8m+4v=49 \\ 8m+4(\frac{21}{2}-\frac{3}{2}m)=49 \end{gathered}[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 8m+4\cdot\frac{21}{2}-4\cdot\frac{3}{2}m=49 \\ 8m+42-6m=49 \end{gathered}[/tex]-Order the like terms together and simplify them:
[tex]\begin{gathered} 8m-6m+42=49 \\ 2m+42=49 \end{gathered}[/tex]-Pass 42 to the right side of the equation by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 2m+42-42=49-42 \\ 2m=7 \end{gathered}[/tex]-Divide both sides by 2 to determine the value of m:
[tex]\begin{gathered} \frac{2m}{2}=\frac{7}{2} \\ m=\frac{7}{2}\approx3.5 \end{gathered}[/tex]-Replace the value obtained for "m" on the expression for "v" to determine the rental cost of one video game:
[tex]\begin{gathered} v=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}\cdot\frac{7}{2} \\ v=\frac{21}{2}-\frac{21}{4} \\ v=\frac{21}{4}\approx5.25 \end{gathered}[/tex]The rental cost for the movies is m=$3.50/movie and the rental cost for the videogames is v=$5.25/video game
Micheal Larry scored 18 points in a basketball game . Micheal scored twice as many points as Larry . How many points did Larry score ?
6 points
Explanations:Let the number of points scored by Michael be m
Let the number of points scored by Larry be l
Michael and Larry scored 18 points together
m + l = 18.........(1)
Michael scored twice as many points as Larry:
m = 2l..........(2)
Substitute equation (2) into equation (1)
2l + l = 18
3l = 18
l = 18/3
l = 6
Larry scored 6 points
The graph below shows the relationship between the number of hours and thenumber of miles jogged.Y161514131211109Miles8322356HoursBased on the information in the graph, what is the unit rate in miles per hour?How did u get the unit rate
Since the graph shows a proportional relationship, in order to find the unit rate in miles per hour, we just need to choose a point in the graph and divide the number of miles by the number of hours.
Looking at the graph, we can choose the point (2.5, 8), so we have:
[tex]\text{unit rate}=\frac{8\text{ miles}}{2.5\text{ hours}}=3.2\text{ miles/hour}[/tex]So the unit rate is 3.2 miles per hour.
If P = (-1, 0, 1, 2, 4} and Q = (4, 5, 6}, find Pu Q.O (-1, 0, 1, 2, 4, 5, 6}Of0 (4)O (-1, 0,1, 2, 4}
Statement Problem: If;
[tex]P=\mleft\lbrace-1,0,1,2,4\mright\rbrace,Q=\mleft\lbrace4,5,6\mright\rbrace[/tex]Find;
[tex]P\cup Q[/tex]Solution:
The union of two sets is a set containing all elements that are in the two sets.
The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Thus, the union of set P and set Q is;
[tex]P\cup Q=\mleft\lbrace-1,0,1,2,4,5,6\mright\rbrace[/tex]
y is the midpoint of xz.x has coordinates (8,-10)and y has coordinates(-12,1)find the coordinates of z
Answer:(-32,12)
Step-by-step explanation:
Find the change in x and change in y from point x to point y. In this case it is -20 for x and +11 for y. Since the definition of a midpoint splits the line into 2 equal segments you can use the changes to calculate z. Use the midpoint coordinates and add the changes like this: (-12-20,1+11) and you will get (-32,12) for z.
Juan and Raj cut up a banana to put on cereal. Juan puts 1/7 of the banana on his bowl of cereal, and Raj puts 2/5 of the banana on his bowl of cereal. What fraction of the banana did Juan and raj put on their cereal.
Juan and Raj put 19/35 fraction of banana on their cereal.
What is a fraction?
A number that represents a rational number is called a common fraction. A decimal, percent, or negative exponent can all be used to represent the same number. For instance, the fraction 1/100 is equivalent to the values 0.01, 1%, and 102. The implicit denominator of an integer can be conceived of as being one (for instance, 7 = 7/1). The term "set of rational numbers" in mathematics refers to the collection of all numbers that can be stated in the form a/b, where a and b are integers and b is not zero. This collection is denoted by the letter Q, which stands for quotient. When a number can be expressed in that way, it is said to be a rational number (i.e., as a common fraction).
1/7 + 2/5
= (5 + 14)/35
= 19/35
Hence, Juan and Raj put 19/35 fraction of banana on their cereal.
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A scale drawing for a restaurant is shown below. In the drawing, 2 I'm represents 3 m. Assuming the dinning hall is rectangular, find the area of the real dining hall
To solve this question, follow the steps below.
Step 01: Find the real measures of the dining hall.
The measure of the drawing is 2cm x 6cm.
Given: 2cm = 3m.
Then, 6cm = 2cm + 2cm + 2cm = 3m + 3m + 3m = 9m
The real measure of the dining hall is 3m x 9m.
Step 02: Find the area of the dining hall.
The dining hall is a rectangle and the area (A) of a rectangle is:
[tex]A=l*h[/tex]Where l and h are the sides of the rectangle.
Then, the area of the dining hall is:
[tex]\begin{gathered} A=3*9 \\ A=27m^2 \end{gathered}[/tex]Answer: The area of the dining hall is 27 m².
Find the value of x that makes m II n [please help I really don't know what to do :') ]
Consider the function f(x)=(x+4)(x+2). Dilate f(x) by x to create a new function of a higher degree.
f(x) = (x+4)(x+2).
f(x) = x² + 2x + 4x + 8
f(x) = x² + 6x + 8
Dilate by x:
x³ + 6x² + 8x
What type of function is shown below? Y=5x
A. both proportional and non-proportional
B. non-proportional
C. neither proportional nor non-proportional
D. proportional
need Answer As Soon As Possible - ASAP
Fill in the missing statement and reason in the proof of the corresponding angles theorem.
It is given that AB is parallel to CD and the points E, G, H and F are collinear.
The measure of angle EGF is 180 degrees.
Now,
Angle AGE+angle AGF=180 degrees.
So, it happends using the addition property of equality.
Now, angle AGF and CHF are the same side interior angle.
Therefore, the correct option is (D)
What ordered pairs do you get when you complete the table ?
for -1:
the equation will be:
[tex]y=3(-1)-1[/tex]and we symplyfy so:
[tex]y=-4[/tex]So the coordinate is:
[tex](-1,-4)[/tex]for 0:
the equation will be:
[tex]y=3(0)-1[/tex]so we simplify:
[tex]y=-1[/tex]so the coordinate is:
[tex](0,-1)[/tex]and for 1:
the equation will be:
[tex]y=3(1)-1[/tex]we simplify:
[tex]y=2[/tex]So the coordinate will be:
[tex](1,2)[/tex]So the answer is A)
Finn, Michael, Luke, and Tommy are going to have a movie night this weekend. Together, they have 33 movies. If they decide to
randomly choose four movies, what is the probability that the four they choose will consist of each of their favorite movies?
Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest
millionth
Answer:
1/982080 as a fraction
0.000001 when rounded to the nearest millionth
Step-by-step explanation:
Each time they pick a movie the odds change
the first pick is 1/33
the second is 1/32
the next is 1/31
the last is 1/30
multiply these fractions
angle Y is inscribed in the circle below. the measure of arc XZ is 205°
SOLUTION:
Case: Circle theorems
Method:
The angle subtended at the center by the arc XZ is twice the value at the circumference at Y
[tex]\begin{gathered} m\angle XOZ=2\times m\angle XYZ \\ 205=2\times Y \\ Y=\frac{205}{2} \\ Y=102.5\degree \end{gathered}[/tex]Final answer:
102.5 degrees
find the image Matrix that represents the rotation of the polygon then graph the polygon and its image
SOLUTION
[tex]\text{The image matrix at 90}^o\text{ rotation is derived using the formula }[/tex][tex]\begin{gathered} \begin{bmatrix}{\cos \theta} & -\sin \theta & {} \\ \sin \theta & {\cos \theta} & {} \\ {} & {} & {}\end{bmatrix}\text{ where }\theta\text{ is 90}^{} \\ \text{This becomes the matrix of } \\ \begin{bmatrix}{0} & {-1} & {} \\ {} & {} & {} \\ {1} & {0} & {}\end{bmatrix}\text{ }\times\text{ }\begin{bmatrix}{2} & {4} & {6}{}{} \\ {2} & {5} & {1}\end{bmatrix}\text{ = }\begin{bmatrix}{0-2} & {0-5} & {0-1}{}{} \\ {2+0} & {4+0} & {6+0}\end{bmatrix}\text{ = } \\ \\ \begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \\ \\ \text{Therefore, the image matrix is }\begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \end{gathered}[/tex]The graph is shown below
help mee pleasee!!
thank you <3
The equation would be y = 20.1x + 359 which represents an estimate of the number of individuals employed as medical assistants in the year.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
We have to determine the slope of the line :
⇒ m = (y₂ - y₁)/(x₂ -x₁ )
⇒ m = (560 - 359)/(10-0)
⇒ m = 20.1
This represents new assistants per year
So y-intercept of 359, your equation becomes
⇒ y = 20.1x + 359
Using the above equation, estimate the number of individuals employed as medical assistants in the year.
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Rajesh is filing single and he has an adjusted gross income (AGI) of $84,000 for the 2018 tax year. He qualifies for the standard deduction of $12,000. Use the following 2018 Federal tax rate schedule to calculate his 2018 Federal income tax.
If your filing status is single;
Rajesh's tax in 2028 is $11,779.50 based on his adjusted gross income (AGI), standard deduction, and filling status.
How to find the tax?First, find the taxable income:
= adjusted gross income (AGI) - standard deduction
= 84,000 - 12,000
= $72,000
This taxable income is in the $38,700 - $82,500 bracket so Rajesh's tax in 2018 would be:
= 4,453.50 + 22% of the excess over $38,700:
Solving for the tax to be paid by Rajesh in 2018 is:
= 4,453.50 + ( 22% x (72,000 - 38,700))
= $11,779.50
In conclusion, the tax that Rajesh would pay in 2018 is $11,779.50.
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help me pleasee!!
thank you
The equation of the line is [tex]f(x) =- \frac{1}{3}x -4[/tex]
How is the equation of the line calculated?
The line passes through the following points,
[tex](x_1,y_1)=(-6, -2)\\\\(x_2,y_2)=(-9,-1)[/tex]
The slope- intercept form of the equation,
y = mx +c ----(1)
(a)What is the slope (m) ?
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-1+2}{-9+6} \\\\m= \frac{1}{-3} \\\\m= -\frac{1}{3}[/tex]
(b) What is the constant ( c) ?
Substituting [tex](x_1,y_1)[/tex] and m in (1)
[tex]y = mx+c\\\\-2 = -\frac{1}{3} (-6)+c\\\\-2 = +2 +c\\\\c = -4[/tex]
Substituting m and c in (1)
y = mx +c
[tex]y =- \frac{1}{3}x -4[/tex]
Using function notation, y = f(x)
The equation of the line is,
[tex]f(x) =- \frac{1}{3}x -4[/tex]
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Please answer with if the slope is positive or negative and what the slope is.
The slope is positive ✨️
Find the Slope and the Y-Intercept of the line with the given equation
Answer: Slope is -4/5 and Y-int is 6
Step-by-step explanation: From the y=mx+b you can see the m is -4/5 and the b is 6. So in this case the slope would be -4/5 and y int would be 6
When we MULTIPLY FRACTIONS, we blank the numerators, blank the denominators and blank if needed.
a. add b. keep c. multiply d. simplify
Answer:
When we multiply fractions, we multiply the numerators, multiply the denominators, and then simplify if needed.
Consider the following pair of points.
(-3, -3) and (2, 9)
Step 1 of 2: determine the distance between the two points.
Step 2 of 2: determine the midpoint of the line segment joining the pair of points.
Answer:
.
Step-by-step explanation:
Which of the following is the equation for a circle with a center of (−2, −3) and a radius of 7?
Okay, here we have this:
Considering the provided information, and that the form of the standard circle equation is (x-h)²+(y-k)²=r², where the centered at (h, k), and radius r, so replacing with the provided data, we obtain:
(x-h)²+(y-k)²=r²
(x-(-2))²+(y-(-3))²=(7)²
(x+2)²+(y+3)²=49
Finally we obtain that the correct answer is the first option
